It is highly likely that most features of Hibernate (i.e. everything except DDL schema generation) will work perfectly with many other relational databases. You may easily add a new SQL dialect by extending the existing dialects. Keep in mind that some features of the query language are not supported for databases which do not have subqueries.

Firebird

Offers many ANSI SQL-92 features, runs on Linux, Windows, and a variety of Unix platforms. Excellent concurrency, high performance, and powerful language support for stored procedures and triggers. It has been used in production systems, under a variety of names since 1981. JDBC type 4 driver with excellent support. DDL statements cannot be executed when there is more than one open JDBC connection. PreparedStatement caching is impossible! Firebird InterClient 2.01 is strongly recommended in preference to other versions of Interbase Interclient. Its also worth trying the latest pure Java "JayBird" driver (http://www.ibphoenix.com).

MySQL

No subselects in "current" versions (subselect support is currently in beta). No transactions with MyISAM tables, only with InnoDB tables (consider changing the default for your databases). The Caucho JDBC driver does not work.

Oracle

Do not use JDBC drivers before version 9.2.0.3 for Oracle 9. These drivers have a round-off bug which strips off any number with decimals (e.g. from 666.67 to 666.0). Oracle JDBC drivers have extremely bad support for large text or binary columns. At least some versions of the Oracle 9i driver handle JDBC timestamps extremely badly - do not use timestamps for optimistic locking, use version numbers.